You pay all costs and follow all normal timing rules for cards played from exile this way
Sacrifice after III.) I All artifacts and creatures phase out
Terror of the Peaks might be the weakest of these three for this deck, only letting you do damage equal to the entering creature's power to any target
Alenni, Brood Recruiter Baru, Fist of Krosa Battle Frenzy Boartusk Liege Cabaretti Charm Catharsis Creakwood Liege Deranged Hermit Glistening Deluge Howlpack Alpha Imperious Perfect Juniper Order Advocate Jyoti, Moag Ancient Kaysa Kinbinding Meng Huo, Barbarian King Murkfiend Liege Nemata, Grove Guardian Nissa, Ascended Animist Paragon of Eternal Wilds Phabine, Boss's Confidant Plane-Merge Elf (playtest) Rank and File Restless Prairie Rouse the Swarm Selesnya Guildmage Silk, Web Weaver Squirrel Wrangler Sylvan Anthem Thelonite Hermit Tolsimir Wolfblood Verdeloth the Ancient Wall Crawl Wilt-Leaf Liege
It would be better as a B enchantment that just said "0: Discard a card from your hand." Speed is nice but in the cube things are a little more rounded
Fire Nation Salvagers can help reanimate multiple cards each combat in a counters deck, provided opponents have them available